BUS352 Chapter 10 Problems

10.7   When people make estimates, they are influenced by anchors to their estimates. A study was conducted in which students were asked to estimate the number of calories in a cheeseburger. One group was asked to do this after thinking about a calorie-laden cheesecake. A second group was asked to do this after thinking about an organic fruit salad. The mean number of calories estimated in a cheeseburger was 780 for the group that thought about the cheesecake and 1,041 for the group that thought about the organic fruit salad. (Data extracted from "Drilling Down, Sizing Up a Cheeseburger's Caloric Heft," The New York Times, October 4, 2010, p. B2.) Suppose that the study was based on a sample of 20 people who thought about the cheesecake first and 20 people who thought about the organic fruit salad first, and the standard deviation of the number of calories in the cheeseburger was 128 for the people who thought about the cheesecake first and 140 for the people who thought about the organic fruit salad first.

a. State the null and alternative hypothesis if you want to determine whether the mean estimated amount of calories in the cheeseburger is lower for the people who thought about the cheesecake first than for the people who thought about the organic fruit salad first.

b. In the context of this study, what is the meaning of the Type I error?

c. In the context of this study, what is the meaning of the Type II error?

d. At the 0.01 level of significance, is there evidence that the mean estimated number of calories in the cheeseburger is lower for the people who thought about the cheesecake first than for the people who thought about the organic fruit salad first?

10.17 Brand valuations are critical to CEOs, financial and marketing executives, security analysts, institutional investors, and others who depend on well-researched, reliable information needed for assessments, and comparisons in decision making. Millward Brown Optimor has developed the BrandZ Top 100 Most Valuable Global Brands for WPP, the world’s largest com-munications services group. Unlike other studies, the BrandZ Top 100 Most Valuable Global Brands fuses consumer measures of brand equity with financial measures to place a financial value on brands. The file BrandZTechFin contains the brand values for two sectors in the BrandZ Top 100 Most Valuable Global Brands for 2014: the technology sector and the financial institutions sector.

a. Assuming that the population variances are equal, is there evidence of a difference between the technology sector and the financial institutions sector with respect to mean brand value? (Use a=.05.)

b. Repeat (a), assuming that the population variances are not equal.

c. Compare the results of (a) and (b).

10.20 Nine experts rated two brands of Colombian coffee in a taste-testing experiment. A rating on a 7-point scale (1 = extremely unpleasing, 7 = extremely pleasing) is given for each of four characteristcs: taste, aroma, richness, and acidity. The following data stored in Coffee contains the ratings accumulated over all four characteristcs: 

a. At the 0.05 level of significance, is there evidence of a difference in the mean ratings between the two brands?

b. What assumption is necessary about the population distribution in order to peform this test?

c. Determine the p-value in (a) and interpret its meaning.   

d. Construct and interpret a 95% confidence interval estimate of  the difference in the mean ratings between the two brands.

10.34 Does co-browsing have positive effects on the customer experience? Co-browsing refers to the ability to have a contact center agent and customer jointly navigate an online document or mobile application on a real-time basis through the web. A study of businesses indicates that 81 of 129 co-browsing organizations use skills-based routing to match the caller with the right agent, whereas 65 of 176 non-co-browsing organizations use skills-based routing to match the caller with the right agent. 

a. At the 0.05 level of significance, is there evidence of a difference between co-browsing organizations and non-co-browsing organizations in the proportion that use skills-based routing to match the caller with the right agent?

b. Find the p-value in (a) and interpret its meaning.

10.47  A bank with a branch located in a commercial district of a city has developed an improved process for serving customers during the noon-to-1 hour lunch period. The waiting time (operationally defined as the time elapsed from when a customer enters the line until he or she reaches the teller window) needs to be shortened to increase customer satisfaction. A random sample of 15 customers is selected, and the results (in minutes) are as follows (and stored in bank 1):

4.21        5.55        3.02        5.13        4.77        2.34        3.54        3.20

4.50        6.10        0.38        5.12        6.46        6.19        3.79

Suppose that another branch, located in a residential area, is also concerned with the noon to 1 lunch period. A random sample of 15 customers is selected, and the results are as follows (and stored in bank 2)

9.66        5.90        8.02        5.79        8.73        3.82        8.01        8.35

10.49     6.68        5.64        4.08        6.17        9.91        5.47

a. Assuming that the population variances from both banks are equal, is there evidence of a difference in the mean waiting time between the two branches? (Use a = 0.05.)

b. Determine the p value in a and interpret its meaning.

c. What assumption about the population distribution of each bank is necessary in (a)? Is the assumption valid for these data?

d. Based on the results of (a), is it appropriate to use the pooled variance t test to compare the means of the two branches?

10.55 Consider an experiment with four groups, with eight values in each. For the ANOVA summary table below, fill in all the missing results:

10.59 A hospital conducted a study of the waiting time in its emergency room. The hospital has a main campus and three satellite locations. Management had a business objective of reducing waiting time for emergency room cases that did not require immediate attention. To study this, a random sample of 15 emergency room cases that did not require immediate attention at each location were selected on a particular day, and the waiting times (measured from check-in to when the patient was called into the clinic area) were collected and stored in ERWaiting.

a. At the 0.05 level of significance, is there evidence of a difference in the mean waiting times in the four locations?

b. If appropriate, determine which locations differ in mean waiting time.

c. At the 0.05 level of significance, is there evidence of a difference in the variation in waiting time among the four locations?